kalman_filter_cpp {kalmanfilter}

Kalman Filter

Description

Kalman Filter

Usage

kalman_filter_cpp(ssm, yt, Xo = NULL, Xs = NULL, weight = NULL, smooth = FALSE)

Arguments

ssm

list describing the state space model, must include names B0 - N_b x 1 matrix, initial guess for the unobserved components P0 - N_b x N_b matrix, initial guess for the covariance matrix of the unobserved components Dm - N_b x 1 matrix, constant matrix for the state equation Am - N_y x 1 matrix, constant matrix for the observation equation Fm - N_b X p matrix, state transition matrix Hm - N_y x N_b matrix, observation matrix Qm - N_b x N_b matrix, state error covariance matrix Rm - N_y x N_y matrix, state error covariance matrix betaO - N_y x N_o matrix, coefficient matrix for the observation exogenous data betaS - N_b x N_s matrix, coefficient matrix for the state exogenous data

yt

N x T matrix of data

Xo

N_o x T matrix of exogenous observation data

Xs

N_s x T matrix of exogenous state

weight

column matrix of weights, T x 1

smooth

boolean indication whether to run the backwards smoother

Value

list of matrices and cubes output by the Kalman filter

Examples

#Nelson-Siegel dynamic factor yield curve
library(kalmanfilter)
library(data.table)
data(treasuries)
tau = unique(treasuries$maturity)

#Set up the state space model
ssm = list()
ssm[["Fm"]] = rbind(c(0.9720, -0.0209, -0.0061), 
                    c(0.1009 , 0.8189, -0.1446), 
                    c(-0.1226, 0.0192, 0.8808))
ssm[["Dm"]] = matrix(c(0.1234, -0.2285, 0.2020), nrow = nrow(ssm[["Fm"]]), ncol = 1)
ssm[["Qm"]] = rbind(c(0.1017, 0.0937, 0.0303), 
                    c(0.0937, 0.2267, 0.0351), 
                    c(0.0303, 0.0351, 0.7964))
ssm[["Hm"]] = cbind(rep(1, 11),
                    -(1 - exp(-tau*0.0423))/(tau*0.0423), 
                    (1 - exp(-tau*0.0423))/(tau*0.0423) - exp(-tau*0.0423))
ssm[["Am"]] = matrix(0, nrow = length(tau), ncol = 1)
ssm[["Rm"]] = diag(c(0.0087, 0, 0.0145, 0.0233, 0.0176, 0.0073, 
                     0, 0.0016, 0.0035, 0.0207, 0.0210))
ssm[["B0"]] = matrix(c(5.9030, -0.7090, 0.8690), nrow = nrow(ssm[["Fm"]]), ncol = 1)
ssm[["P0"]] = diag(rep(0.0001, nrow(ssm[["Fm"]])))
    
#Convert to an NxT matrix
yt = dcast(treasuries, "date ~ maturity", value.var = "value")
yt = t(yt[, 2:ncol(yt)])
kf = kalman_filter(ssm, yt, smooth = TRUE)